Log-concavity and the maximum entropy property of the Poisson distribution

By Oliver Johnson. 2006

90 citations recorded by the source corpus.

We prove that the Poisson distribution maximises entropy in the class of ultra log-concave distributions, extending a result of Harremoes. The proof uses ideas concerning log-concavity, and a semigroup action involving adding Poisson variables and thinning. We go on to show that the entropy is a concave function along this semigroup.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e44cfe5be88e5f220f2bdff87e65cb1c087e8a08

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Paul-Marie Samson
2. Adrien Saumard
3. Cyril Roberto
4. Jon A. Wellner
5. Prasad Tetali
6. Nathael Gozlan
7. Ying Zhang
8. Guillaume P. Dehaene

In Mathematical Physics

1. Cyril Roberto
2. Paul-Marie Samson
3. Adrien Saumard
4. Jon A. Wellner
5. Prasad Tetali
6. Nathael Gozlan

In Statistics and Probability

1. Nathael Gozlan
2. Cyril Roberto
3. Prasad Tetali
4. Paul-Marie Samson
5. Adrien Saumard
6. Jon A. Wellner
7. John C. Duchi
8. Richard J. Samworth

Citations in the corpus

• Displacement convexity of entropy and related inequalities on graphs (2012, methodology): “The construction of this interpolating path is inspired by a certain binomial interpolation due to Johnson [20], see also [17, 18, 19].”
• Log-Concavity and Strong Log-Concavity: a review (2014, methodology): “proof is given by Johnson [2007] using results from Kontoyiannis, Harremoës and Johnson [2005] and Efron [1965], and that is the proof we will summarize here.”